Since the standard symmetrized variance \(\widehat{V}(\rho )\)  is a
concave function of the vector \((\rho _{00},\ldots ,\rho _{d-1,d-1})^\) ,
where \(\rho _{ii}=\left\langle i \left| \rho  \right| i \right\rangle \) , and is invariant under the
permutation \(P_{\pi }\) , \(\widehat{V}(\rho )\)  is a measure of
uncertainty which quantifies the uncertainty associated with the
quantum state \(\rho \)  in the framework of uncertainty measure
[1]}. In Refs. [2]}, [3]},  the authors proposed the idea to split the uncertainty into
quantum part and classical part. In Refs. [2]},  the total uncertainty is specified to the variance of
observable \(A\)  in state \(\rho \) , while the quantum uncertainty is
specified to the Wigner-Yanase skew information. Here we can
decompose the standard symmetrized variance \(\widehat{V}(\rho )\)  into
the quantum uncertainty \(Q(\rho )\)  and the classical uncertainty
\(C(\rho )\) ,
\(\widehat{V}(\rho )=C(\rho ) + Q(\rho ),\) 
